Primarily (but not exclusively) in the field of natural resources exploration, there is a requirement to measure the absolute value and variation of gravity at a given point and over an area gradient, thereby detecting the presence of sub-surface anomalies which give rise to the variation in the measured gravity value. In order to provide a portable, accurate, efficient and cost effective method for making the measurements, a gravity sensing apparatus can be deployed hosted by a variety of vehicles, such as (for example, but not limited to) an aircraft or helicopter, with compensation applied by a motion sensing apparatus to reduce or eliminate the effects of vibration and vehicle motion and structural flexure on the gravity and gravity gradiometry data.
To assist in the discussion of the background to the invention, the following definitions and calculations apply:—
One Standard Gravity is defined as the free-fall acceleration of a body at mean sea level and at a latitude of 45.5° and is 9.80665 m/s2. In SI units, One Gal is a unit of acceleration, equal to 1 cm per sec squared. Therefore one milliGal ( 1/1000 of a Gal, and written mGal) is 1/1000 of 1 cm/s2. Therefore 1 mGal is 1.0197 μg, and one Standard Gravity is 980.665 Gal.
The vertical gravity gradient (variation with height) above Earth's surface is approximately 3.1 μGal per meter of height, resulting in a maximum difference of about 2 Gal from the top of Mount Everest to sea level. Changes in latitude and elevation cause a variation of gravity value from (typically) 976 to 983 Gal.
For measurement of gravity go where the terrain is at mean sea level and at latitude ØgØ=9.780327(1+0.0053024 sin2 Ø−0.0000058 sin2 2Ø) m·s−2 
However, the gravity sensor will be flying at (typically) 100 meters above mean sea level (AMSL). The first correction to this formula is therefore the free air correction (FAC), which accounts for heights above sea level. Gravity decreases with height, at a rate which near the surface of the Earth is such that linear extrapolation would give zero gravity at a height of one half the radius of the Earth, i.e. the rate is 9.80665 m·s−2 per 3086 km. Thus:—gØ=9.780327(1+0.0053024 sin2 Ø−0.0000058 sin2 2Ø)−h*3.086*10−6 m·s−2 
where h=height in meters above mean sea level.
Note that for flat terrain above sea level a second term is added, for the gravity due to the extra mass. For this purpose the extra mass can be approximated by an infinite horizontal slab, and we get 2πG times the mass per unit area, i.e. 4.2×10−10 m3·s−2·kg−1 (0.042 μGal·kg−1·m2)) (the Bouguer correction).
For a mean rock density of (say) 2.67 g·cm−3 this gives 1.1×10−6 s−2 (0.11 mGal·m−1). Combined with the free-air correction this means a reduction of gravity at the surface of circa 2 μm·s−2 (0.20 mGal) for every meter of elevation of the terrain. (Note that the two effects would cancel at a surface rock density of 4/3 times the average density of the whole Earth.)
For the gravity below the surface we have to apply the free-air correction as well as a double Bouguer correction. With the infinite slab model this is because moving the point of observation below the slab changes the gravity due to it to an opposite value.gØ=9.8061999−0.0259296 cos(2Ø)+0.0000567 cos2(2Ø) m·s−2 
Taking a geological example, the gravitational anomaly of an ore body of density contrast 300 kg m-3 and of dimension 200 meters buried at a depth of 100 meters would be circa 2*10−6 ms−2, or 0.00002% of the normal Earth gravity field (0.2 μg).
Note that gradiometer data is usually presented scaled in Eotvos (Eo), where 1 Eo is 0.1 mGal/km. Thus the Eotvos is a unit of gravity gradient, and 1 Eotvos corresponds to 10−9 s−2.
There are numerous examples in the prior art of mechanisms employed for the measurement of gravity (a gravimeter) (i.e. LaCoste & Romberg—Scintrex, Inc., AIR-SEA II Dynamic Gravity Meter). In the simplest (and possibly the oldest) form, a mass attached to a beam or a spring can be used, with the natural (linear) deflection of the beam or spring being proportional to the value of the gravity field applied to the beam or spring and associated mass. A degree of damping will be applied to the beam or spring, reducing the sensitivity but also the settling time.
In more recent times, the MEMS (Micro-Electro-Mechanical Systems) accelerometer and associated electronic interface provides a means of measuring small accelerations of the order discussed above.
When a gravimeter is used for airborne measurements, the multi-axis movements and structural flexure of the aircraft will modify the natural accelerations due to any change in gravity registered as the aircraft moves over terrain, and these modifications must be compensated for when the gravity data is processed. For example, vertical “bounce” caused by air turbulence will produce accelerations many times greater than those resulting from changes in the gravity value. Air turbulence and the resulting airframe movement will also cause the structure of the aircraft (principally the wings in relation to the fuselage) to flex, introducing vertical accelerations which will modify the gravity values read by the gravity sensors. With any given pilot, the aircraft will precess in a cyclic manner along its flight path at a frequency determined by the flight characteristics of the airframe and the human control lag employed. Variations in aircraft attitude will change the perceived “downward” direction through the aircraft floor, and therefore the gravimeter sensor must employ some form of attitude stabilisation in order to maintain a true vertical reference.
In practical terms, an aircraft will be used to survey a defined area, and normally in a fixed pattern of flight lines of known position and orientation. At the end of each line, the aircraft executes a turning manoeuvre to position itself for the next line. It is desirable to enter each line with a positionally stable sensor, and therefore (depending on the sensor damping employed) the aircraft will extend the approach path to the line start. This might result (for a relatively small survey area) in a large increase in the line length, increasing cost and reducing survey capability for a given fuel load, and therefore it is desirable to minimise the effects of settling time following an aircraft manoeuvre.
For measurement of the gravity gradient (a gradiometer), the sensors employed are of a similar nature to those used simply for gravity, but are usually more sensitive, and are often used in pairs mounted a defined distance apart, thereby allowing the gravity gradient to be measured.
Again in the prior art, there are examples of gradiometers (Air-FTG from Bell Geospace Ltd, Falcon from Fugro AS) which use pairs of accelerometers mounted at a (small) fixed distance apart (and in a temperature and attitude controlled enclosure) on a slowly rotating disc, thereby assisting in the process of noise cancellation and balancing out any differences in accelerometer sensitivity. Both systems use three co-located discs with a total of 12 accelerometers (4 per disc mounted 10 cm apart) in a single (large and heavy) attitude and temperature stabilised assembly. Published results of a comparison of the two systems (ASEG-PESA Airborne Gravity Workshop 2004, Australian Government, ISBN: 1 920871 13 6) show both systems to be capable of reporting gradients of the order 7 Eo with a 700 m cut-off (Air-FTG) and 8 Eo with a 400 m cut-off (Falcon) over a test area with a range of gradients up to 70 Eo.
U.S. Pat. No. 5,357,802 (Hoffmeyer) describes a gradiometer using pairs of accelerometers rotating on a disc at about 15 rpm, and suggests an increase in rotational speed would improve noise performance. US Patent application 20040211255, (Leeuwen H. et al, October 2004) describes a similar system using a single larger disc (0.6 meters diameter) with up to 72 accelerometers rotating at about 15 rpm, thereby improving noise performance over a smaller disc, and suggests sensitivities might be obtained in the order of 10 Eo. Cryogenic gravity gradiometers have been proposed using atomic resonance techniques, again mounted on attitude stabilisation platforms (ArKex Ltd, EGG System).
A common feature of most current and proposed gravity and gravity gradiometry systems is the size and weight of the apparatus—most are relatively large compared to the size of the typical (small) geophysics survey aircraft often employed to host them. A floor area of 2 square meters is common, with the combined weight of the sensor, thermal and attitude management systems and processing electronics approaching or often exceeding 200 kg. Relative to the scale of the geological features being measured, all are single point measurement systems.